Question

Draw a straight line AB of length 8 cm. Draw the locus of all points which are equidistant from A and B. Prove your statement.

Answer 1

CD represents the locus of all points that are equidistant from A and B.

Consider triangles GOA and GOB.

∠GOA = ∠GOB (each is 90°).

OG = OG (common side).

AO = OB (because CD is the perpendicular bisector of AB at O).

Thus, by the SAS similarity criterion, ΔGOA is similar to ΔGOB.

Since the triangles are similar, the ratios of their corresponding sides are equal:

`(AG)/(OG) = (BG)/(OG)`

= AG = BG

Hence, AG = BG.

This proves that every point on CD is equidistant from A and B.